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Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method

Author

Listed:
  • Zaineb Yakoub

    (National Engineering School of Gabes, University of Gabes, Gabes 6029, Tunisia)

  • Omar Naifar

    (Control and Energy Management Laboratory, National School of Engineering, Sfax University, Sfax 3038, Tunisia)

  • Dmitriy Ivanov

    (Department of Mechatronics, Samara State University of Transport, 443066 Samara, Russia
    Department of Information Systems Security, Samara National Research University, 443086 Samara, Russia)

Abstract

In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated least squares algorithm. The basic concept is to remove the imposed bias by including a correction term into the least squares estimations. The suggested approach makes a significant contribution by the estimation, iteratively, of fractional order system coefficients as well as the orders and the time-delay using a nonlinear optimization algorithm. The main advantage of this method is to provide a simple and powerful algorithm with good accuracy. The suggest method performances are assessed through two numerical examples.

Suggested Citation

  • Zaineb Yakoub & Omar Naifar & Dmitriy Ivanov, 2022. "Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method," Mathematics, MDPI, vol. 10(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:3028-:d:894760
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    References listed on IDEAS

    as
    1. Zaineb Yakoub & Omar Naifar & Messaoud Amairi & Manel Chetoui & Mohamed Aoun & Abdellatif Ben Makhlouf & Jerzy Baranowski, 2022. "A Bias-Corrected Method for Fractional Linear Parameter Varying Systems," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-14, April.
    2. Omar Naifar & Abdellatif Ben Makhlouf, 2021. "On the Stabilization and Observer Design of Polytopic Perturbed Linear Fractional-Order Systems," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-6, March.
    3. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
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    Cited by:

    1. Limin Zhang & Junpeng Li & Wenting Zhang & Junzi Yang, 2022. "Identification of Nonlinear State-Space Systems via Sparse Bayesian and Stein Approximation Approach," Mathematics, MDPI, vol. 10(19), pages 1-18, October.

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